0.242424… as a Fraction

0.242424… (0.24 repeating) as a fraction is 8/33.

How to convert 0.242424… to a fraction

  1. Let x = 0.242424... (the underlined part, 24, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 24.242424...
  3. Subtract to cancel the repeating tail: 100x − x = 24 − 0, so 99x = 24.
  4. Solve: x = 24/99. The greatest common divisor is 3, so x = 8/33.

Check

Divide 8 by 33 on a calculator: 8 ÷ 33 = 0.2424242424… which matches 0.242424….

Similar repeating decimals

DecimalFraction
0.222…2/9
0.230230230…230/999
0.232323…23/99
0.2333…7/30
0.234234234…26/111
0.2444…11/45
0.252525…25/99
0.2555…23/90

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.